Rerolling Magic Items
Contents
Basics
Affix Level
Affix Chances
Cube CharmsBasicsConsider the recipe,
3 Perfect Gems (any type and mixture) + Magic Item (any type) 
New Magic Item (of the same type)listed on the Arreat Summit Horadric Cube page:
http://classic.battle.net/diablo2exp/items/cube.shtml. Rerolling a magic item with 3 perfect gems is sometimes referred to as cubing.
ilvl and PropertiesThe above recipe
preserves ilvl (ilvl of output = ilvl of input). Hence, given a sufficient supply of perfect gems, you can keep rerolling a magic item and always have the exact same odds of rolling what you want. Notice how this is fundamentally different from recipes in which the ilvl is either fixed at a lower value or degraded with each roll.
Only the ilvl of the Magic Item matters when rerolling with perfect gems.
The New Magic Item will acquire random properties, determined by item type and ilvl.Character level, difficulty, player count etc. do not matter. The game was not designed to obey your rumours; it does not care what you like or how you think it should be. Horadric Cube recipes are explained in
CubeMain.txt (download and install ATMA V to view this and other game files) and the above recipe explicitly states to use 100 % of the ilvl.
The ilvl, while not visible in-game, may be determined, depending on how the item was obtained (dropped, gambled, shopped).
- Monster drops: ilvl = mlvl (monster level).
For monster levels, check the Treasure Classes guide, sections: "Monster TCs" (subsection: "Monster Level (mlvl)") , "SuperUniques and Bosses".
- Gambled items: ilvl = clvl - 5 + rnd(10) (character level). That is, from clvl - 5 to clvl + 4, uniformly distributed (10 % chance of each).
The ilvl of gambled items is capped below at 5 and above at 99.
Maximum resell value in Gold (Act 1, ... , Act 5),
- Normal: 5k, 10k, 15k, 20k, 25k
- Nightmare: 30k
- Hell: 35k
The results of gambling are unaffected by vendor. Gamble in Hell.
Chest and rack drops, both of which are hardly ever used in practice: ilvl = Alvl or ilvl = Alvl - 1 (area level).
Affix LevelWhen an item with affixes is generated, in this case a
magic item, the item's affix level (alvl) is calculated from ilvl and qlvl (base item quality level, see below). Based on alvl and item type, the game looks up the available affixes. Every affix has a
level, the minimum alvl which the item must meet to have a chance of acquiring that affix. Higher alvl ~ larger affix pool.
Magic items receive 1 prefix, 1 suffix, or 1 of each. Due to differences in affix frequencies, some affixes are more likely to spawn than others.
Check my profile:
Diablo II Resources Item Statistics Affix Tables.
Affix Level CalculationCode
IF(magiclvl > 0)
(1) THEN alvl = max{ilvl,qlvl} + magiclvl
ELSE IF(max{ilvl,qlvl} < 99 - int(qlvl/2))
(2) THEN alvl = max{ilvl,qlvl} - int(qlvl/2)
(3) ELSE alvl = 2*max{ilvl,qlvl} - 99
; ilvl and alvl are capped at 99
Ref: Basin Wiki, D2 Affix Level Chart,
http://wiki.theamazonbasin.com/index.php/D2_Affix_Level_ChartOnly Circlets, Sorceress Orbs, Staves, and Normal + Exceptional Wands have magiclvl > 0,
- Circlet (qlvl 24): magiclvl = 3
- Coronet (qlvl 52): magiclvl = 8
- Tiara (qlvl 70): magiclvl = 13
- Diadem (qlvl 85): magiclvl = 18
- Sorceress Orbs + Staves: magiclvl = 1
Normal + Exceptional Wands: magiclvl = 1
Quality levels (qlvl) are listed as
Quality Level on the Arreat Summit Weapons and Armor pages:
http://classic.battle.net/diablo2exp/items/weaponsandarmor.shtml.
For Jewelry (values from
Misc.txt),
- Amulet, Ring, Jewel: qlvl = 1
- Small Charm: qlvl = 28
- Large Charm: qlvl = 14
- Grand Charm: qlvl = 1
Let's state some key results derived from the affix level formulae above.
Amulet, Ring, Jewel, Grand CharmSince these have qlvl 1, the term, int(qlvl/2) is 0 and hence, if ilvl < 99, (2) alvl = ilvl, otherwise (ilvl = 99): (3) alvl = 2*ilvl - 99 = 99 = ilvl. Thus, alvl = ilvl no matter what.
Amulet, Ring, Jewel, and Grand Charm: alvl = ilvl.Each of the +2 to [class] Skill Levels / Skills prefixes on Amulets are level 90 (highest affix). Which means you cannot gamble a +2 to [class] Skill Levels / Skills Amulet before clvl 86. And just 3 monsters in the game are mlvl 90 or higher: Hell Diablo {mlvl 94}, Nihlathak {mlvl 95}, and Baal {mlvl 99}.
The latter also applies when we consider the Grand Charm suffix, "of Vita": +41-45 to Life (level 91). On a related note, each of the +1 to [skilltab] prefixes on Grand Charms are level 50. The first area in the game having level 50 regular monsters is the Nightmare Great Marsh (Act 3). At this level, the GCs can even get as much as +26-30 to Life.
Circlet, Coronet, Tiara, DiademSince these have magiclvl > 0, we get (1) alvl = max{ilvl,qlvl} + magiclvl. Suppose again, we look at the +2 [class] Skill Levels / Skills prefixes (level 90, highest affix on Circlets). We obtain the following results,
Any Circlet, Coronet, or Tiara of at least ilvl 87, 82, or 77, respectively, may acquire any affix.
Since max{ilvl,85} + 18 > 99, any Diadem will have alvl 99, regardless of ilvl.Monarch (qlvl 72)
Suppose we want a
Jeweler's Monarch of Deflecting (JMoD),
- "Jeweler's" (level 55)
Socketed (4)
- "of Deflecting" (level 11)
+30 % Faster Block Rate
+20 % Increased Chance of Blocking
We need to know the minimum ilvl corresponding to at least alvl 55. According to the affix level formulae, it is first checked whether
max{ilvl,qlvl} < 99 - int(qlvl/2). Inserting qlvl = 72, we get max{ilvl,72} < 63. This is impossible, so (3) is used. Since we want alvl >= 55,
2*max{ilvl,72} - 99 >= 55 <=> max{ilvl,72} >= 77
Hence, we need a
Monarch of
at least ilvl 77 to have even the slightest chance of rolling a JMoD.
Affix ChancesIn practice, we may want a range of sufficient ilvls rather than restricting ourselves to one value. For instance, when cubing for the +41-45 to Life suffix ("of Vita", level 91) on a
Grand Charm, it makes no difference if the charm is ilvl 94 (Hell Diablo), ilvl 95 (Hell Nihlathak), or ilvl 99 (Hell Baal); each one satisfies ilvl >= 91, and there are no higher affixes.
Depending on item type and desired affix(es), in some cases using an ilvl greater than necessary means that we expand the affix pool and thus risk rolling higher (unwanted) affixes. To have the best possible odds, we should use at least the required minimum ilvl, but less than the ilvl corresponding to a higher affix if we want to prevent it from spawning.
Aside from this, we rely solely on the Wheel of Fortune.
Affix FrequenciesWhen a magic item is generated, the game has to determine if it gets a prefix only, a suffix only, or both. In doing so, it uses the following probabilities,
- Prefix (P) only: 25 %
- Suffix (S) only: 50 %
- Prefix + Suffix (P+S): 25 %
Next, it picks affixes accordingly, as either P, S, or P+S has been selected,
- Affixes are picked from the pool corresponding to the alvl
- If P+S was chosen, P and S are selected independently of each other
- Each affix has its own affix frequency (weight), the relative likeliness to be chosen
- When an affix has several possible values which may spawn, the game picks one at random
- The chance to pick a certain affix is the affix frequency divided by the sum of affix frequencies (P or S)
Refer to the Affix Tables for affix frequencies (see the reference in the previous section).
Code
Affix chances
(4) Prob_P = 1/4 * frequency_P / sum_P
(5) Prob_S = 1/2 * frequency_S / sum_S
(6) Prob_P+S = 1/4 * frequency_P / sum_P * frequency_S / sum_S
; frequency_X: the sum of affix frequencies corresponding to the desired affixes (prefixes or suffixes).
; sum_X: the sum of all affix frequencies (prefixes or suffixes available for the given ilvl, respectively).
Use the option
calculate Affix-Chances in the Affix Tables to confirm the results below.
DON'T FORGET to set the
Item-Level (ilvl).
Grand CharmSuppose we had one drop from a regular monster in the Nightmare Great Marsh. Since ilvl = mlvl = Alvl = 50 and alvl = ilvl, this charm has alvl 50, just sufficient to generate any of the +1 to [skilltab] prefixes (level 50), which, according to the Affix Tables, have frequency 1 each. Let's determine the odds of rolling any of the +1 to [skilltab] ([class] Only) prefixes.
ilvl 50: sum_P = 230. A prefix can spawn either alone or combined with a suffix. With 21 (7 x 3) desired prefixes, frequency_P = 21, and no suffix (or any), (4) and (6) yield,
- Chance = Prob_P + Prob_P+S = (1/4 + 1/4) * frequency_P / sum_P = 1/2 * 21/230 = 21:460 ~ 4.57 %
If we further demand a specific +1 to [skilltab] prefix, the odds are 21 times lower:
1:460 ~
0.22 %. Don't be too surprised if you have to spend hundreds of perfect gems rolling for a specific "skiller".
MonarchHere is an excellent opportunity to effectively waste your perfect gems:
Jeweler's Monarch of Deflecting (JMoD). Assume we were fortunate enough to come by an ilvl 77
Monarch, granting us the best possible odds. Using the Affix Tables, we get
ilvl 77: sum_P = 158, sum_S = 135; "
Jeweler's": frequency = 1, "
of Deflecting": frequency = 6.
From (6),
- Chance = Prob_P+S = 1/4 * 1/158 * 6/135 = 1:14220 ~ 0.00703 %
Kickass odds, eh ?
